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A111314 a(n) = a(n-1) + a(n-2) + 2 where a(0) = a(1) = 1. 6
1, 1, 4, 7, 13, 22, 37, 61, 100, 163, 265, 430, 697, 1129, 1828, 2959, 4789, 7750, 12541, 20293, 32836, 53131, 85969, 139102, 225073, 364177, 589252, 953431, 1542685, 2496118, 4038805, 6534925, 10573732, 17108659, 27682393, 44791054, 72473449 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is the sequence A(1,1;1,1;2) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. - Wolfdieter Lang, Oct 17 2010

LINKS

T. D. Noe, Table of n, a(n) for n=0..500

Wolfdieter Lang, Notes on certain inhomogeneous three term recurrences. - Wolfdieter Lang, Oct 17 2010

FORMULA

a(n) = 2*Fib(n+1)-Fib(n+2)+Fib(n+3)-2. - Robert G. Wilson v, Nov 10 2005

G.f.: (2x^2-x+1)/((x-1)(x^2+x-1)). - T. D. Noe, Oct 19 2007

a(n) = F(n-1)+F(n+3)-2, where F(n) is the n-th Fibonacci number. - Zerinvary Lajos, Jan 31 2008

a(n) = 3*Fib(n+1)-2. - Olivier Pirson, Jun 30 2015

MAPLE

with(combinat): seq(fibonacci(n-1)+fibonacci(n+3)-2, n=0..35); # Zerinvary Lajos, Jan 31 2008

MATHEMATICA

a[0] = a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + 2; Table[ a[n], {n, 0, 36}] (* Robert G. Wilson v *)

PROG

(Sage) from sage.combinat.sloane_functions import recur_gen2b; it = recur_gen2b(1, 1, 1, 1, lambda n: 2); [it.next() for i in xrange(1, 38)] # Zerinvary Lajos, Jul 09 2008

CROSSREFS

Cf. A000045, A000071.

Sequence in context: A190805 A008471 A156622 * A139217 A038391 A073832

Adjacent sequences:  A111311 A111312 A111313 * A111315 A111316 A111317

KEYWORD

easy,nonn

AUTHOR

Parthasarathy Nambi, Nov 03 2005

EXTENSIONS

More terms from Robert G. Wilson v, Nov 07 2005

STATUS

approved

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Last modified September 23 17:46 EDT 2017. Contains 292362 sequences.